Is it feasible to train a Machine Learning Model (with image inputs) in an average personal computer?
You may play around on an average laptop but training will be very slow and you will be limited on the size of your model.
Once you try to build something more serious you will run out of memory very fast. A system with a GPU is recommended if you want to really do things like image recognition. If you buy something I would not go for any GPU with less than 8 GB memory and for an X99 motherboard to keep the flexibility to add a second GPU on full speed later if needed.
Don't mix up image recognition running on phones etc. Those are trained models and actually just being applied that is much easier process. Training is way much more expensive.